arXiv subjects

Jad Doghman

Publications and source records attributed to Jad Doghman.

3 recordsLinked to original sources

arXiv2022

Convergence of the stochastic Navier-Stokes-$α$ solutions toward the stochastic Navier-Stokes solutions

Loosely speaking, the Navier-Stokes-$α$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $α$. Starting from a strong two-dimensional solution to the Navier-Stokes-$α$ model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier-Stokes equations under the condition $α$ goes to 0. The initially introduced probability space and the Wiener process are maintained throughout the investigation, thanks to a local monotonicity property that abolishes the use of Skorokhod's theorem. High spatial regularity a priori estimates for the fluid velocity vector field are carried out within periodic boundary conditions.

math.AP↗

arXiv2022

Numerical approximation of the stochastic Navier-Stokes equations through artificial compressibility

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $ε$. Space and time are discretized through a finite element approximation and an Euler method. The convergence analysis of the suggested numerical scheme is investigated throughout this paper. It is based on a local monotonicity property permitting the convergence toward the unique strong solution of the Navier-Stokes equations to occur within the originally introduced probability space. Justified optimal conditions are imposed on the parameter $ε$ to ensure convergence within the best rate.

math.NA↗

arXiv2021

Numerical and convergence analysis of the stochastic Lagrangian averaged Navier-Stokes equations

The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$α$) equations of incompressible fluid turbulence with multiplicative random forcing, under nonperiodic boundary conditions within a bounded polygonal (or polyhedral) domain of R^d , d $\in$ {2, 3}. The convergence analysis of a fully discretized numerical scheme is investigated and split into two cases according to the spacial scale $α$, namely we first assume $α$ to be controlled by the step size of the space discretization so that it vanishes when passing to the limit, then we provide an alternative study when $α$ is fixed. A preparatory analysis of uniform estimates in both $α$ and discretization parameters is carried out. Starting out from the stochastic LANS-$α$ model, we achieve convergence toward the continuous strong solutions of the stochastic Navier-Stokes equations in 2D when $α$ vanishes at the limit. Additionally, convergence toward the continuous strong solutions of the stochastic LANS-$α$ model is accomplished if $α$ is fixed.

math.NA↗